Internal problem ID [11929]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 5(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } \tan \left (x \right )+\cot \left (x \right ) y=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 1, y^{\prime }\left (\frac {\pi }{4}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 3.828 (sec). Leaf size: 46436
dsolve([diff(y(x),x$2)+tan(x)*diff(y(x),x)+cot(x)*y(x)=0,y(1/4*Pi) = 1, D(y)(1/4*Pi) = 0],y(x), singsol=all)
\[ \text {Expression too large to display} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]+Tan[x]*y'[x]+Cot[x]*y[x]==0,{y[Pi/4]==1,y'[Pi/4]==0}},y[x],x,IncludeSingularSolutions -> True]
Not solved